Details

sample1.7s

Algorithm

intervals

Results

847.0ms	252×	body	10240	exit
405.0ms	91×	body	2560	valid
158.0ms	85×	body	1280	valid
100.0ms	504×	body	80	nan
38.0ms	37×	body	640	valid
16.0ms	25×	body	320	valid
7.0ms	14×	body	160	valid
1.0ms	4×	body	80	valid
0.0ms	1×	body	320	nan

simplify101.0ms

Calls

1 calls:

Slowest

100.0ms

(acos (pow (fmod (cosh a) (* a a)) (log1p a)))

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.4b

localize38.0ms

Local error

Found 2 expressions with local error:

59.4b	(fmod (cosh a) (* a a))
2.3b	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

2×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`
1×	`acos-asin`

Calls

2 calls:

Slowest

3.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
2.0ms	(fmod (cosh a) (* a a))

series18.0ms

Calls

2 calls:

Slowest

14.0ms	(fmod (cosh a) (* a a))
3.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))

simplify180.0ms

Calls

6 calls:

Slowest

67.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
52.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
39.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
7.0ms	(fmod (cosh a) (pow a 2))
7.0ms	(fmod (cosh a) (pow a 2))

prune308.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 59.0b

localize52.0ms

Local error

Found 3 expressions with local error:

59.4b	(fmod (cosh a) (* a a))
13.1b	(log (exp (fmod (cosh a) (* a a))))
2.3b	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-exp-log` `log-pow`
3×	`log-prod` `exp-prod` `add-cbrt-cube` `insert-posit16` `add-log-exp`
2×	`rem-log-exp`
1×	`acos-asin`

Calls

3 calls:

Slowest

4.0ms	(log (exp (fmod (cosh a) (* a a))))
2.0ms	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
0.0ms	(fmod (cosh a) (* a a))

series11.0ms

Calls

3 calls:

Slowest

4.0ms	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
4.0ms	(log (exp (fmod (cosh a) (* a a))))
3.0ms	(fmod (cosh a) (* a a))

simplify408.0ms

Calls

17 calls:

Slowest

60.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
55.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
44.0ms	(log (sqrt (exp (fmod (cosh a) (* a a)))))
44.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
32.0ms	(sqrt (fmod (cosh a) (* a a)))

prune527.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 59.0b

localize40.0ms

Local error

Found 4 expressions with local error:

59.4b	(fmod (cosh a) (* a a))
59.4b	(fmod (cosh a) (* a a))
11.8b	(log (exp (sqrt (fmod (cosh a) (* a a)))))
2.3b	(acos (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `*-un-lft-identity` `log-pow` `add-cube-cbrt`
6×	`exp-prod`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp`
3×	`log-prod` `sqrt-prod`
2×	`rem-log-exp`
1×	`acos-asin`

Calls

4 calls:

Slowest

3.0ms	(log (exp (sqrt (fmod (cosh a) (* a a)))))
1.0ms	(acos (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))
0.0ms	(fmod (cosh a) (* a a))
0.0ms	(fmod (cosh a) (* a a))

series19.0ms

Calls

4 calls:

Slowest

13.0ms	(log (exp (sqrt (fmod (cosh a) (* a a)))))
3.0ms	(acos (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))
2.0ms	(fmod (cosh a) (* a a))
2.0ms	(fmod (cosh a) (* a a))

simplify543.0ms

Calls

23 calls:

Slowest

51.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
49.0ms	(log (* (cbrt (exp (sqrt (fmod (cosh a) (* a a))))) (cbrt (exp (sqrt (fmod (cosh a) (* a a)))))))
39.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
38.0ms	(exp (sqrt (fmod (cosh a) (* a a))))
36.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))

prune657.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 59.0b

localize39.0ms

Local error

Found 4 expressions with local error:

59.4b	(fmod (cosh a) (* a a))
59.4b	(fmod (cosh a) (* a a))
11.8b	(log (exp (sqrt (fmod (cosh a) (* a a)))))
1.3b	(- (/ PI 2) (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
7×	`log-pow` `add-cube-cbrt`
6×	`exp-prod` `add-log-exp`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube` `insert-posit16`
3×	`log-prod` `sqrt-prod`
2×	`rem-log-exp` `difference-of-squares`
1×	`asin-acos` `sub-neg` `times-frac` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `associate--r-`

Calls

4 calls:

Slowest

11.0ms	(- (/ PI 2) (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a))))
3.0ms	(log (exp (sqrt (fmod (cosh a) (* a a)))))
0.0ms	(fmod (cosh a) (* a a))
0.0ms	(fmod (cosh a) (* a a))

series47.0ms

Calls

4 calls:

Slowest

30.0ms	(- (/ PI 2) (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a))))
13.0ms	(log (exp (sqrt (fmod (cosh a) (* a a)))))
2.0ms	(fmod (cosh a) (* a a))
2.0ms	(fmod (cosh a) (* a a))

simplify3.6s

Calls

30 calls:

Slowest

511.0ms	(sqrt (sqrt (fmod (cosh a) (* a a))))
296.0ms	(- (sqrt (/ PI 2)) (sqrt (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))))
292.0ms	(+ (/ (sqrt PI) (sqrt 2)) (sqrt (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))))
292.0ms	(/ (exp (/ PI 2)) (exp (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))))
287.0ms	(- (/ PI 2) (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a))))

prune896.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 59.0b

regimes493.0ms

Accuracy

0% (0.1b remaining)

Error of 59.2b against oracle of 59.1b and baseline of 59.2b

bsearch7.0ms

end0.0ms

sample34.1s

Algorithm

intervals

Results

19.9s	7996×	body	10240	exit
7.1s	3191×	body	2560	valid
3.1s	2531×	body	1280	valid
2.2s	16194×	body	80	nan
893.0ms	1217×	body	640	valid
311.0ms	599×	body	320	valid
121.0ms	349×	body	160	valid
20.0ms	113×	body	80	valid
18.0ms	7×	body	5120	nan
10.0ms	7×	body	2560	nan
7.0ms	8×	body	1280	nan
3.0ms	4×	body	640	nan
3.0ms	11×	body	160	nan
3.0ms	6×	body	320	nan